Best way to look at this is;

Casual Gamer.... buy PS4, you can play all the games and it costs less.

Enthusiast Gamer... buy PS4K, you will probably appreciate the performance bump and make good value of the extra spend.

Essentially they are now segmenting the market and catering to two different types of gamers. It gives more choice and does not take anything away from anyone.
Just because there is a new model, doesn't take any features, games or performance from your base PS4. If you got angry that games ran better on PC, you wouldn't be taken seriously. Why would you get angry that there is a new PS4 releasing?
When the PS3 Fat 60GB stopped being offered, people lost features, now Sony are offering more options and people are complaining.....

"Acording to the new rumors, ps4 Neo won´t have exclusives, won´t have new pheripherals, won´t have new content, games just will be the same but will look better or have more fps than standar PS4. "

You answered the question yourself

It is a PS4. That Should answer the question.

All this gen console crap dont matter.
Generations is about time periodes and thats it.
If the NX releases and its competitors are the PS4 and the XB1, that doesnt make it a gen up on them.
Not if its capabilitys are the sames as the others on the market.
It just makes it late to the party.

A PS4k in the same vain, will not be a new gen.
Its the same gen we have now, and stays that way until we have a PS5 & XB2.

Since it doesn't exist, it is not a new gen.

Definitely not 9th gen. It's just a slight update to the 8th gen console. My question is if the games, being made specifically for the original PS4, will look or perform better.

This...

Still 8th gen cause it's still a PS4.

Just like how all of the other 3DS models are still the same.

Imho PS NEO will be 8th gen as long as it doesn't get major exclusives, just like N3DS is 8th gen because it got just a handful of exclusives.

Still 8th gen and almost low end hardware again x'D